Question

The dimensions of $\sigma b^4$ are (where $\sigma =$ Stefan's constant and $b=$ Wein's constant)

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M{L}^4{T}^{-3}\right]$
• C. $\left[M{L}^{-2}T\right]$
• D. $\left[M{L}^6{T}^{-3}\right]$

Answer 1

Answer: (B)

${\lambda }_{m}T=b$ or $b^4={\lambda }_m^4{T}^4$
and $\frac{\text{ Energy }}{\text{ Area }\times \text{ Time }}=\sigma T^4$
or $\sigma =\frac{\text{ Energy }}{(\text{ Area }\times \text{ Time })T^4}$
or $\sigma b^4=\left(\frac{\text{ Energy }}{\text{ Area }\times \text{ Time }}\right){\lambda }_m^4$
$\therefore \left[\sigma b^4\right]=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right][T]}\left[L^4\right]$
$=\left[M{L}^4{T}^{-3}\right]$